In a promising sign for the Bay Area’s housing recovery, the number of underwater homes in the region fell at the fastest rate in at least two years during the third quarter, according to a report released Wednesday.

The drop pulled 42,000 homes in the East Bay, Peninsula and South Bay into the black, so that their homes are worth more than the mortgages on them, the online real estate company Zillow reported.

Only Contra Costa County is at roughly the national average of one in five homes in negative equity, Zillow said.

“The movement is unalloyed great news for the housing market,” said Zillow’s chief economist, Stan Humphries.

In the past year, 103,000 homes have emerged from underwater status in the four counties of San Mateo, Santa Clara, Alameda and Contra Costa, Zillow said.

Only 13.3 percent of Alameda County homes were underwater in the third quarter, down from 19.3 percent in the second quarter, Zillow said. In Contra Costa County, 19 percent were underwater, down from 26.8 percent. Santa Clara County dropped from 10.6 percent to 7.2 percent and San Mateo went from 9.8 percent to 6.8 percent.

Housing experts are hoping that the trend toward increasing equity will help cure a chronic shortage of homes for sale. The housing market has been crimped by low inventory partly because large numbers of homeowners couldn’t sell except at a loss.

Glen Bell with Better Homes & Gardens Mason-McDuffie Real Estate in Berkeley, said he expects homeowners who are finally in positive territory to put their homes on the market in the spring.

“There are people now that couldn’t refinance, couldn’t get out of their house because they were upside-down, and maybe couldn’t qualify for a short sale,” Bell said. “Now they’re in position to sell their house.”

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